Find between which two integers the given rational numbers lie.
a)15/17 b) -34/16
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Since there are infinitely many rational numbers between two distinct real numbers, there are many ways to find just a few. Here’s one way…
Find the difference between the two numbers, 5/3 - 3/2 = 1/6 in this case. Then divide that by 6, to get 1/36 in this case, so we can construct 6 intervals between the two numbers with 5 rational numbers as the boundaries. This gives the 5 numbers:
3/2+1/36 = 55/36, 3/2+2/36=14/9, 3/2+3/36=19/12, 3/2+4/36=29/18, and finally the 5th number is 3/2+5/36=59/36.
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